In general, no.
Affairs are entered into consensually by two people, knowing that there is a third person being cheated on. There is an unwritten contract between you and your lover to keep it secret. If you don't like that, you shouldn't have started the affair.
If you are now feeling angry with the lover, and want to strike back or harm him/her, there is a strong temptation to reveal all to hurt him. But such vindictiveness reflects more on the immaturity of the angry person (you) than on the lover.
If possible, deal with the issue between the two of you.
And in future, avoid affairs. Affairs suit few people, and usually end in tears.
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